mlsanityData to 7 Oct 2026

Higher-order organization of complex networks

arXiv 1612.08447 ↗First posted 26 Dec 2016cs.SI cs.DM physics.soc-phcited by 109

Not on the map. Why?

Abstract (arXiv)

Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks---at the level of small network subgraphs---remains largely unknown. Here we develop a generalized framework for clustering networks based on higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns.

Key facts. Cited by 109 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Dec 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 28; 2022: 21; 2023: 14; 2024: 15; 2025: 14; 2026: 17.

109 papers.

Sort:

By area:

  1. 2021Inductive Representation Learning in Temporal Networks via Causal Anonymous Walkscited by 188
  2. 2021You are AllSet: A Multiset Function Framework for Hypergraph Neural Networkscited by 124
  3. 2021MagNet: A Neural Network for Directed Graphscited by 104
  4. 2024Position: Graph Foundation Models are Already Herecited by 84
  5. 2021Size-Invariant Graph Representations for Graph Classification Extrapolationscited by 82
  6. 2021Generative hypergraph clustering: from blockmodels to modularitycited by 48
  7. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 45
  8. 2022Making Recommender Systems Forget: Learning and Unlearning for Erasable Recommendationcited by 27
  9. 2023TempME: Towards the Explainability of Temporal Graph Neural Networks via Motif Discoverycited by 27
  10. 2022Higher-order Clustering and Pooling for Graph Neural Networkscited by 26
  11. 2022Heterogeneous manifolds for curvature-aware graph embeddingcited by 23
  12. 2022I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphscited by 20
38 more
  1. 2023Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classificationcited by 19
  2. 2021A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinationscited by 18
  3. 2021Motif Prediction with Graph Neural Networkscited by 18
  4. 2021DPPIN: A Biological Repository of Dynamic Protein-Protein Interaction Network Datacited by 17
  5. 2023From Hypergraph Energy Functions to Hypergraph Neural Networkscited by 17
  6. 2022Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphscited by 15
  7. 2023A survey and taxonomy of loss functions in machine learningcited by 15
  8. 2023Boosting Multitask Learning on Graphs through Higher-Order Task Affinitiescited by 15
  9. 2021Machine learning dismantling and early-warning signals of disintegration in complex systemscited by 14
  10. 2023Curvature-based Clustering on Graphscited by 14
  11. 2021Neural Predicting Higher-order Patterns in Temporal Networkscited by 13
  12. 2021Latent Space Model for Higher-order Networks and Generalized Tensor Decompositioncited by 13
  13. 2022Inference of hyperedges and overlapping communities in hypergraphscited by 13
  14. 2024TopoGCL: Topological Graph Contrastive Learningcited by 13
  15. 2021A nonlinear diffusion method for semi-supervised learning on hypergraphscited by 11
  16. 2021Motif Graph Neural Networkcited by 10
  17. 2021MotifClass: Weakly Supervised Text Classification with Higher-order Metadata Informationcited by 9
  18. 2022Hypergraph Artificial Benchmark for Community Detection (h-ABCD)cited by 9
  19. 2021Local Hyper-Flow Diffusioncited by 8
  20. 2021Recommender systems based on graph embedding techniques: A comprehensive reviewcited by 8
  21. 2021Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Modelcited by 7
  22. 2022Deep Hypergraph Structure Learningcited by 7
  23. 2021Disentangling homophily, community structure and triadic closure in networkscited by 6
  24. 2021Local Algorithms for Finding Densely Connected Clusterscited by 6
  25. 2022Sparse random hypergraphs: Non-backtracking spectra and community detectioncited by 5
  26. 2023Multi-grained Hypergraph Interest Modeling for Conversational Recommendationcited by 5
  27. 2024Representation Learning for Frequent Subgraph Miningcited by 5
  28. 2021Nonparametric Modeling of Higher-Order Interactions via Hypergraphonscited by 4
  29. 2022Skew-Symmetric Adjacency Matrices for Clustering Directed Graphscited by 4
  30. 2022The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networkscited by 4
  31. 2023Compressed Interaction Graph based Framework for Multi-behavior Recommendationcited by 4
  32. 2023DeSCo: Towards Generalizable and Scalable Deep Subgraph Countingcited by 4
  33. 2024Financial Default Prediction via Motif-preserving Graph Neural Network with Curriculum Learningcited by 4
  34. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  35. 2024Hypergraph Attacks via Injecting Homogeneous Nodes into Elite Hyperedgescited by 4
  36. 2021PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Countscited by 3
  37. 2022CHIEF: Clustering with Higher-order Motifs in Big Networkscited by 3
  38. 2022Scalable Motif Counting for Large-scale Temporal Graphscited by 3

50 most cited of 109 All 109 (JSON)